Given a 1G+1G  population, the branching ratios of the 1G+2G  and 2G+2G  populations are determined by the fraction of 1G+1G  merger products that are retained in the cluster.
During the coalescence of a binary black hole, the anisotropic emission of GWs imparts a kick on the remnant.
The magnitude of the kicks depends sensitively on the spin and mass ratio of the binary [1]}, [2]}, [3]}, [4]}, [5]}, and can far exceed the typical escape velocities of globular clusters (\(\sim 30\) –\(50~\mathrm {km\,s}^{-1}\)  at \(z=0\) ), ejecting merger products and leaving them unavailable to form new generations of binary black holes [6]}, [7]}, [8]}.
Therefore, the branching ratios of the 1G+2G  and 2G+2G  popoulations are sensitive to the distribution of mass ratios and component spins in the 1G+1G  population, as well as the mass and size of the cluster.
